# Velocity-Definition, Types, Practice Problems, FAQs

## What is Velocity?

The change in position vector or the displacement of a body divided by the time taken is called velocity. In the following diagram, the position vector of the body changes from point A to B. Displacement is defined as the shortest possible distance between two points. Motion between two points A and B

Imagine yourself cycling in a circular path of radius r as shown in figure.

Distance between points Displacement between points It is a vector quantity. Velocity carries a SI unit of Velocity of an object is said to be positive if the body moves in the positive direction, and negative if it moves in the negative direction.

## Velocity vs Speed

Though both of them have the same units, yet they are totally different. Speed is scalar, whereas velocity is a vector.

## Average Velocity

The total displacement covered by a body divided by the total time taken is called average velocity(vavg). In the following displacement time (s-t) graph, the average velocity in the time interval ab is equal to the slope of the graph between a and b.  s indicates the displacement undergone in time t.

## Instantaneous Velocity

The velocity of an object(v) at a particular instant of time is called “instantaneous velocity vinst ”. If ds indicates displacement in time dt, then indicates the derivative of displacement with respect to time at a given point, P in our case.

The graphical meaning of at point P is the slope of the graph at point P i.e the slope of the tangent drawn on the s-t curve at point P. Direction of instantaneous velocity at an instant is the same as the direction of average velocity for a straight-line motion if the body does not reverse its direction of motion. Direction of instantaneous velocity at an instant may be opposite to the direction of average velocity for a straight line motion if the body reverses its direction of motion. ## Uniform and Non-Uniform Motion

A motion is said to be uniform if the body covers equal distance in equal intervals of time. For eg. if a body covers 2 m of distance each second, the body is said to be in uniform motion. Whereas a motion is said to be non-uniform if the body covers unequal distances in equal intervals of time. A body in non-uniform motion is said to have acceleration.

## Relative Velocity

Motion is never absolute; it is always “relative”. It can only be defined wrt an observer. So, relative velocity is defined as the velocity of one body with respect to another.

The relative velocity of A wrt B can be written as ## Practice Problems of Velocity

Question 1.  A car A moves along east with a velocity of 20 ms-1. Another car B moves west with a speed of 40 ms-1. The relative velocity of A wrt B has magnitude

(a)20 ms-1 (b)10 ms-1 (c)60 ms-1 (d) 25 ms-1  Question 2.  A police van is moving on a highway with a speed of 30 kmhr-1 fires a bullet at a thief car which is moving away in the same direction with a speed of 190 kmhr-1. If the muzzle speed of the bullet is 150 ms-1, find the speed of the bullet with respect to the thief's car.

Answer: Muzzle velocity of the bullet  Since bullet is fired from the police car, the velocity of bullet, Velocity of the bullet with respect to the thief, Question 3. A particle moves along the x-axis. At a time t, the displacement is given by x=40+12t-t3. It’s x coordinate when it comes to rest?

(a) 24 m  (b) 40 m (c) 56 m (d) 16 m

When it comes to rest, velocity=0 Question 4.  A car travels with a velocity vu from X to Y. It returns from Y to X with a velocity vd. What is the average velocity of the car during this entire trip? Since the displacement for the entire trip is zero, average velocity is zero.=

## FAQs of Velocity

Question 1. What is velocity?

Answer: Velocity is defined as the change in displacement divided by the change in time.

Question 2. Is velocity a scalar or vector quantity?

Answer: Velocity is a vector quantity. It has direction.

Question 3.  What is the difference between velocity and speed?

Answer: Velocity is total displacement divided by the total time taken. Speed is the total distance divided by the total time taken. Speed is a scalar quantity whereas velocity is a vector quantity.

Question 4.  Is average velocity greater than average speed?

Answer:  Since distance is greater than or equal to the magnitude of displacement, average speed is greater than or equal to average velocity.

## NCERT Class 11 Physics Chapters

 Physical World Units and Measurements Motion in a Straight Line Motion in a Plane Laws of Motion Work Energy and Power Particles and Rotational Motion Gravitation Mechanical Properties of Solids Mechanical Properties in Liquids Thermal Properties of Matter Thermodynamics Kinetic Theory Oscillations Waves